Guaranteed Privacy of Distributed Nonconvex Optimization via Mixed-Monotone Functional Perturbations

In this letter, we introduce a new notion of guaranteed privacy for distributed nonconvex optimization algorithms. In particular, leveraging mixed-monotone inclusion functions, we propose a privacy-preserving mechanism which is based on deterministic, but unknown affine perturbations of the local objective functions. The design requires a robust optimization method to characterize the best accuracy that can be achieved by an optimal perturbation. This is used to guide the refinement of a guaranteed-private perturbation mechanism that can achieve a quantifiable accuracy via a theoretical upper bound that is independent of the chosen optimization algorithm. Finally, simulation results illustrate the accuracy-privacy trade-off and that our approach outperforms a benchmark differentially private distributed optimization algorithm in the literature.